Question: Simplify the following expression and state the condition under which the simplification is valid: $k = \dfrac{n^2 - 4n - 60}{n^2 + 6n}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 4n - 60}{n^2 + 6n} = \dfrac{(n - 10)(n + 6)}{(n)(n + 6)} $ Notice that the term $(n + 6)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n + 6)$ gives: $k = \dfrac{n - 10}{n}$ Since we divided by $(n + 6)$, $n \neq -6$. $k = \dfrac{n - 10}{n}; \space n \neq -6$